BGE: hold at last frame
In your code rigM will be constantly true when the right mouse button is held down. This means the action will keep playing. Try changing bge.logic.KX_INPUT_ACTIVE  to bge.logic.KX_INPUT_JUST_ACTIVATED in your definition for rigM.

Give the breathing animation a lower priority by setting the priority argument on your playaction call to a high number. See the Game Types API Reference for details. If you don't want other actions to play while the right mouse button is held down then change your logic to not play the action when rigM is true.